Binary Superlattices from Colloidal Nanocrystals and Giant

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Binary Superlattices from Colloidal Nanocrystals and Giant Polyoxometalate Clusters Maryna I. Bodnarchuk,*,†,‡ Rolf Erni,§ Frank Krumeich,† and Maksym V. Kovalenko*,†,‡ †

Institute of Inorganic Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, CH-8006 Zürich, Switzerland Laboratory for thin films and photovoltaics and §Electron Microscopy Center, EMPA − Swiss Federal Laboratories for Materials Science and Technology, CH-8600 Dübendorf, Switzerland

‡

S Supporting Information *

ABSTRACT: We report a new kind of long-range ordered binary superlattices comprising atomically defined inorganic clusters and colloidally synthesized nanocrystals. In a model system, we combined surfactant-encapsulated, nearly spherical giant polyoxometalate clusters containing 2.9 nm polyoxomolybdate or 2.5 nm polyoxovanadomolybdate cores with monodisperse colloidal semiconductor nanocrystals (PbS, CdSe, PbS/CdS; 4−11 nm). The results are rationalized on the basis of dense packing principles of sterically stabilized particles with predominantly hard-spherelike interparticle interactions. By varying the size-ratios and relative concentrations of constituents, we obtained known thermodynamically stable binary packings of hard-spheres such as NaCl, AlB2, and NaZn13 lattices and also CaCu5-type lattice and aperiodic quasicrystals with 12-fold symmetry. These results suggest that other kinds of cluster materials such as fullerenes and magic-sized metallic and semiconductor clusters can also be integrated into supramolecular assemblies with nanocrystals. Furthermore, synergistic effects are expected from the combination of redox and catalytic properties of polyoxometalates with excitonic and plasmonic properties of inorganic nanocrystals. KEYWORDS: Nanocrystals, clusters, polyoxometalates, self-assembly, superlattices, colloids

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electronic, optoelectronic, luminescent, catalytic, and other devices and applications. Selected recent examples may include synergistic and shape effects in reduction of oxygen catalyzed by binary Pd−Pt NC superlattice,14 enhanced thermal stability of a binary superlattice as compared to disordered mixtures leading to improved magneto-transport properties in Fe3O4FePt binary NC system,15 collective dipolar magnetic interactions in metal ferrite binary NC superlattices,16 fluorescence quenching due to plasmon-exciton interactions in CdSe-Au NC superlattices17 and directionally controlled fusion of NC building blocks into two-dimensional crystals.18 While all-NC superlattices are now well-studied, here we turn reader’s attention to the possibility of combining NCs with other types of building blocks of comparable dimensionality. In this Letter, we report a general methodology for the construction of a new family of superlattices comprising sub5 nm atomically defined polyoxometalate clusters (POMs) and sub-10 nm inorganic NCs, as illustrated in Figure 1a,b. In the footstep of the colloidal crystallization of nano- and sub(micrometer)-sized particles, we show that entropy-directed assembly leads to a variety of hybrid cluster/nanocrystal superlattices, bridging the gap between atomic/molecular crystals and colloidal assemblies. Our choice of POMs as

rystallization of a matter has long been a major thrust in chemistry, biochemistry, and materials science with comparable importance at all length scales ranging from atoms (10−10 m) to large biomolecules (10−8−10−5 m). Recently, a new research field of “artificial solids” has emerged from the self-assembly of highly uniform colloidal inorganic nanocrystals (NCs, typically 3−20 nm, size dispersions below 10%) into long-range ordered superlattices.1 Considering spherical NCs dispersed in nonpolar medium as a predominantly studied system, their excellent size and shape uniformity allows spontaneous formation of single-component,1c,2 binary1,3 or even ternary1e,4 and quasicrystalline structures5 upon evaporation of the solvent. The details of the crystallography,1f,6 thermodynamics,7 and kinetics8 of NC self-assembly have attracted broad interest of the scientific community. Computer simulations are utilized to explain the stability of the known superlattices and to predict new thermodynamically stable binary superlattices of spherical NCs.9 Many key features of conventional atomic and molecular crystals, such as faceting, twinning, polymorphism, and so forth, have been observed also in NC superlattices.10 Presently, great efforts are dedicated to transforming NC superlattices into useful solid state materials11 by developing large-area assembly methods12 and by improving electronic coupling using small capping ligands and molecular linkers.13 A unique combination of stoichiometry and symmetry, along with structural diversity, may provide many possibilities for designing novel materials for © XXXX American Chemical Society

Received: January 20, 2013 Revised: March 12, 2013

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Figure 1. (a) Building blocks for POM/NC superlattices: PbS nanocrystal and {Mo132} giant Keplerate cluster (complete chemical formula including cations is shown in the text); (b) schematics of the POM/NC superlattices with NaCl-type unit cell (the presence of surfactant monolayers is omitted for clarity) and (c) a typical TEM image of [100]-oriented NaCl-type superlattice; (d) space-filling diagram for NaCl, AlB2, CaCu5, and NaZn13 binary crystals. Arrows in (d) indicate the range of {Mo132}/PbS NC size ratios (γeff = 0.41, 0.51, 0.58, 0.74) examined in this study.

First we discuss the design principle of NC/POM superlattices. The lessons learned from the NC self-assembly suggest that for achieving successful coassembly of POMs and NCs into long-range ordered superlattice, two requirements need to be fulfilled by chemical design: (i) solubility of POMs and NCs in the same solvent and (ii) minimization of undesired specific POM-NC and NC-NC interactions such as electrostatic repulsion and strong Van-der-Waals attraction in order to prevent phase-separation of NCs and POMs. At the same time, strong short-range steric repulsion in combination with appropriate size ratio of building blocks is required for obtaining hard-sphere-like interparticle potential and entropy driven crystallization. (i). Solubility and Miscibility. As synthesized, POMs are strongly hydrophilic, polyanionic species. We therefore used a surfactant-encapsulation by providing a dense hydrophobic monolayer of organic cations on the cluster surface, leading to high solubility in common nonpolar solvents such as toluene or chlorobenzene. These solvents also readily solubilize oleatecapped PbS NCs. Surfactant-encapsulation was carried out in a similar manner to Volkmer et al,28b by replacing NH4+ cations with hydrophobic dodecyldimethylammonium cations (DDA), generating (DDA)40(NH4)2{Mo132} (see Supporting Information for details). Notably, DDA+ is the shortest alkylammonium cation that can provide high solubilility of POMs in chlorobenzene. Dialkyl (2Cn) substituted ammonium cations with 12 ≤ n ≤ 16 generally performed better than 1Cn, 3Cn, 4Cn counterparts, which can be best explained by the good match between the molecule cross section and the density of negatively charged surface sites.31 Simplicity and generality of such noncovalent surfactant-encapsulation make it especially appealing. For instance, alkylammonium−POM complexes are intensely studied as amphiphilic building blocks for well-defined nano- and microscale supramolecular assemblies (disks, cones, tubes) due to hydrophobic−hydrophilic interactions with the each other and with the solvents.19d,23 Dynamic light scattering measurements indicate that DDA+-encapsulated {Mo132} clusters form stable dispersions without noticeable aggregation before and after surfactant-encapsulation. Furthermore, complete neutralization of the surface charges in nonpolar solvent due to the tight ionic pairing is evident from electrophoretic mobility measurements (Supporting Information Figure S3) and allows the formation of single-component POM super-

building blocks stems from their seemingly endless structural diversity, suitable dimensions, and their emergent properties.19 To the latter, widely researched catalytic properties of POMs include photocatalytic and electrocatalytic water splitting by ruthenium, cobalt- and tantalum-containing polytungstates,20 epoxidation of olefins with H2O2 catalyzed by silicontungstates,21 POM-catalyzed aqueous oxidation of lignin by molecular oxygen,22 or catalytic desulfurization.23 Further reviews and examples of the catalytic oxidation reactions using POMs can be found in ref.19b,24 Diverse properties of POMs also include single-molecule magnetism, thermo- and elecrochromism.19 POMs can also serve as soluble nanoscale precursors for synthesizing corresponding metal oxides25 and as macroionic and supramolecular building blocks for constructing open frameworks26 and ionic crystals with controlled sorption properties.27 Chemical Design of POM/NC Superlattices. As a smaller constituent of a superlattice, we employed molybdenum-based POM cluster (1),28a for simplicity denoted as {Mo132} according to the total number of Mo atoms. It contains a 2.9 nm polyanionic core with t he composition {Mo132O372Ac30(H2O)n}42−, where n is typically 72. Also known as giant Keplerate cluster, first synthesized by A. Müller and co-workers in 1990s,28 {Mo132} remains the largest known quasi-spherical inorganic cluster.29 As a second example, we have used a mixed molybdenum−vanadium 2.5 nm POM cluster (2), denoted as {Mo72V30}, and synthesized according to Hill and co-workers.30 The structure and purity of the clusters have been confirmed by X-ray diffraction and compared to the calculated patterns (Supporting Information Figure S1). (NH4)42 [Mo72 VIMo60 V O372 (CH3COO)30 (H 2O)72 ]· ca.300 H 2O·ca.10CH3COONH4

(1)

Na8K16(VO)(H 2O)5 [K10 ⊂ {(Mo)Mo5O21(H 2O)3 (SO4 )}12 (VO)30 (H 2O)20 ]·150H 2O

(2)

As a larger component of a superlattice, we used 4.7−10.7 nm oleate-capped PbS NCs with narrow size distributions of ∼5% (Supporting Information Figure S2), allowing convenient tuning of the POM-to-NC size ratio in the range of 0.41−0.74. For comparison, other semiconductor (CdSe, PbS/CdS) and metallic (Au, Pd) NCs were tested as well (all shown in Supporting Information). B

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lattices after the solvent evaporation (Supporting Information Figure S2). (ii). Interparticle Interactions and Size Ratios. For obtaining suitable conditions for coassembly of POMs and NCs, we have chosen a solvent-evaporation based method,1a which is commonly used growing single-component and binary NC superlattices from their colloidal solutions. To minimize undesired interparticle interactions such as strong long-range electrostatic repulsion or attraction, monolayer-protected, electrostatically neutral POMs and NCs were dispersed in nonpolar solvents, where NCs are colloidally stabilized primarily by short-range steric repulsion. Recent studies on binary NC superlattices showed that both entropy and energetic interactions govern the assembly of colloidal NCs,7,32 contributing to the change of the Gibbs free energy of the system, ΔG = ΔH − TΔS. The gain in free volume entropy upon ordering is greater than the decrease in configurational entropy, thus providing a net positive change in the system’s entropy. In the case of binary mixtures, the gain in free volume entropy is proportional to the packing density of the lattice and favors the formation of the densest structure at a given size ratio of spheres (Figure 1d). The packing density for a given binary crystal structure is a function of the effective size ratio between smaller and larger spheres (i.e., γeff = dPOM/dNC, Figure 1d). In the hard sphere approximation (i.e., small enthalpic factor due to weak interparticle interactions), this purely entropic effect favors the formation of highly dense NC superlattices isostructural with various known atomic, ionic or intermetallic phases such as AlB2, NaZn13 and NaCl. These structures were also found in natural as well as artificial opals built of micrometer-large SiO2 spheres, and induced much interest in materials science since the early 1980s.33 Presently available theoretical studies on noninteracting hard spheres predict thermodynamic stability for the following structures:32,34 for 0.41 ≤ γeff ≤ 0.45 NaCl-type lattice is stable, for 0.45 ≤ γeff ≤ 0.61 AlB2 structure is stable; for 0.54 ≤ γeff ≤ 0.63 NaZn13 (ico-AB13) is stable and for 0.76 ≤ γeff ≤ 0.84 only Laves phases are considered to be stable. At these size ratios, NaCl, AlB2 and NaZn13 are the most compact binary lattices with space filling factor exceeding 0.74, corresponding to single component face-centered cubic (fcc) or hexagonal close packing (hcp). Yet the profound interparticle energetics such as dispersive (van der Waals) forces leads to the higher contribution of the enthalpic factor and a greater diversity of stable structures with lower packing densities such as CuAu, Cu3Au, Fe4C, CaCu5, CaB6 and bcc-AB6 lattices,1b,35 which are not predicted to be thermodynamically stable in the mixtures of hard spheres. Notably, a plethora of other forces can be present in the system (dipole−dipole, dipole−induced dipole, magnetic, electrostatic, etc.), all contributing to the interparticle potentials.36 The van der Waals potential between two nanoparticles A and B with radii RA and RB at the distance of the closest approach D is37

VvdW

⎧ ⎪ A⎪ S =− ⎨ + ⎤ D 12 ⎪ D⎡1 + 1+ ⎥ ⎪ ⎣⎢ 2(RA + RB) ⎦ ⎩

1 D S

+

D2 4RARB

⎛ ⎡ ⎤ ⎞⎫ D ⎜ D⎢⎣1 + 2(R + R ) ⎥⎦ ⎟⎪ ⎪ A B ⎟⎬ + 2 ln⎜ ⎜⎜ R ⎡1 + D + D2 ⎤ ⎟⎟⎪ ⎦ ⎠⎪ S 4RARB ⎥ ⎝ ⎢⎣ ⎭

where A is the Hamaker constant and S = 2RARB/(RA + RB) is the reduced radius. Hence the strength of dispersive forces increases with the size and with Hamaker constant. Being strongly related to dielectric function of the material, Hamaker constants for metals such as gold and silver (1−3 eV) are considerably higher than for metal oxides or semiconductors (∼0.3 eV for CdSe).38 For two dissimilar materials Hamaker constant can be approximated as A = (A1A2)1/2. These simple considerations have strong implications onto NC self-assembly. Metallic NCs are always used as a smaller, usually sub5 nm, constituent of binary superlattices in combination with larger, 5−15 nm, semiconductor or metal oxide NCs. This way the magnitude of dispersive A−A, B−B, and A−B forces is comparable, preventing phase separation into single-component lattices and allowing the change of entropy to play a more pronounced role. In agreement with this reasoning, mixtures of POMs with 4−6 nm Au or Pd NCs completely phase separated upon solvent evaporation, while successful coassembly occurred in nearly every sample containing PbS or CdSe NCs. It should be noted that uncertainty in the experimentally determined size ratios is one of the weakest points in accurate examination of the packing principles reflected by space-filling curves (Figure 1d). For example, for a typical combination of monodisperse 5 and 10 nm NCs with size dispersions as narrow as 5%, the resulting “polydispersity” of γeff size ratios is ∼10%, not including the uncertainties in the shell thicknesses. In this regard, the use of atomically defined molecular clusters as a smaller component reduces the problem to the sizedistribution of the larger NC constituent. Effective diameters of NCs and POMs were calculated taking into account the effective thickness of the ligand shell (dNC = dcore + 2dshell). For a dense monolayer of DDA cations on POM surfaces, an effective thickness is estimated to be 1.2 nm, fully consistent with the literature on densely packed hydrophobic monolayers on alumosilicates and surfactant-encapsulated POMs.31,39 For NCs, the ligand shell thickness was estimated as half the mean interparticle distance in a single-component fcc superlatitice: 1.25 nm for 4.7 and 6.6 nm oleic acid capped PbS NCs and 1.1 nm for 8.1 and 10.7 nm oleic acid capped-PbS NCs. We studied four effective size ratios of POMs and NCs targeting the typical existence range of binary superlattices (γeff ≈ 0.4−0.8): 0.41 (10.7 nm PbS NCs), 0.51 (8.1 nm PbS NCs), 0.58 (6.6 nm PbS NCs), and 0.74 (4.7 nm PbS NCs). The particle POM-to-NC number ratios were varied in the range of 1:1 to 20:1 in order to enable all possible superlattice stoichiometries to crystallize. Growth and Structural Characterization of POM/NC Superlattices. POM/NC superlattices were grown using standard solvent-evaporation technique by drying the dispersion of NCs and POMs directly above the carbon-coated transmission electron microscopy (TEM) grid in a tilted vial. Alternatively, we used evaporation at the liquid−air interface12a by layering NC/POM dispersion on the surface of water, C

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Figure 2. Detailed structural characterization of AlB2-type POM/NC superlattice constructed from DDA-encapsulated {Mo132} clusters and 6.6 nm oleate-capped PbS NCs (γeff =0.58). (a,e,h) TEM images; (b,k) HAADF-STEM images at various magnifications; (c,d) crystallographic models of [001] and [100] oriented AlB2 thin-film crystallites; (f,i) images obtained by template analysis of TEM images (e,h); (g,j) small-angle electron diffraction patterns; (l) EDX maps for Mo (red, K-line) and Pb (blue, L-line); (m) EDX line scans for Pb and Mo taken along the line shown in (k).

followed by the solvent evaporation and transfer of the “superlattice membrane” onto the TEM grid. It should be noted, that conventional bright-field TEM imaging suffers from the poor mass−thickness contrast of POMs. Not only is the atomic number of Mo much lower than for Pb (42 vs 82), but also the number of metal atoms is by 1−2 orders of magnitude smaller: 132 Mo atoms in {Mo132} versus ∼1250 Pb atoms in 5 nm PbS NC and ∼10 000 in 10 nm PbS NC. As a result, {Mo132} clusters are poorly visible in the images of POM/NC superlattices. To improve the signal-to-noise ratio of the TEM images in order clearly visualize {Mo132} clusters in copresence of PbS NCs and the amorphous carbon support film, we carried out template matching and averaging of periodic subareas of TEM images based on local cross-correlations (see details in the Supporting Information, Figure S4).40 Obtained images are illustrated throughout this Letter and Supporting Information (Figures 2f, 2i, 3c, 4c, S9d, S13c). Further, in order to determine the crystal structure of the superlattice and possible preferential orientation of the PbS NCs, small- and wide-angle electron diffraction patterns were recorded at large and small camera lengths (Figure 2g,j, Supporting Information Figures S8 and S9e). Diffraction patterns were then compared to simulated ones for a specific lattice orientation. Scanning transmission

electron microscopy (STEM) was used to record high-angle annular dark-field images (HAADF), which are sensitive to the atomic number (Z-contrast) and, therefore, further help to visualize clusters and NCs. Typical HAADF-STEM images for AlB2 and AB13 lattices are shown in Figure 2 and Supporting Information Figure S19. Finally, the position-dependent energy dispersive X-ray (EDX) spectroscopy in STEM mode was used to map the elements in the form of 2D-maps and line scans. Observed POM/NC Superlattices. In the following, we discuss observed POM/NC superlattices and compare with conventional binary NC superlattices. For {Mo132}/PbS NC superlattices in the range of studied size ratios 0.41 ≤ γeff ≤ 0.74, we observed all phases which are known to be thermodynamically stable phases for hard-sphere packings: NaCl (Figure 1c, Supporting Information Figures S5e and S6), AlB2 (Figure 2, Supporting Information Figures S5d, S7, S15, and S16) and NaZn13 (Figure 3, Supporting Information Figures S9 and S14). In addition, we observed minute amounts of bcc-AB6 crystals at γeff = 0.41 (Supporting Information Figure S5f) and domination of CaCu5-type structure at highest γeff of 0.74 (Figure 4, Supporting Information Figure S17). No binary superlattices were observed or could be image-resolved when using smaller PbS NCs (3−4.5 nm, γeff > 0.74). Finally, D

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Figure 5. Dodecagonal quasicrystalline ordering in binary mixtures of 8.1 nm PbS NCs and 2.9 nm DDA-encapsulated {Mo132} clusters (γeff = 0.51): (a, b) TEM images and (c) FFT pattern.

Densest AlB2- and AB13-Type Superlattices in POM/ PbS NC System. AlB2-type lattice with the highest known packing density of all binary crystals is observed in {Mo132}/ PbS NC binary system at γeff = 0.51 (Supporting Information Figures S5d and S7) and at γeff = 0.58 (Figure 2) at a POM-toNC concentration ratio of ≤10. Figure 2 illustrates detailed structural analysis of {Mo132}/PbS NC superlattice exhibiting two low-index projections of AlB2 lattice ([001] and [100]). While the position of PbS NCs is apparent from mass− thickness and diffraction contrast in TEM images (Figure 2a), the position of Mo clusters can be optimally resolved after image processing by template analysis of TEM images (Figure 2f,i), from Z-contrast in HAADF-STEM images (Figure 2b,k), and by elemental mapping with STEM-EDX (Figure 2l,m). At the same size ratio of γeff = 0.58, NaZn13-lattice coexists with AlB2 structure (Figure 3a−d).The structure-directing factor is the relative concentration of each component in a colloidal solutions: a large ∼15−20 fold excess of POM clusters favored the formation of NaZn13 lattice. Together, NaZn13 and AlB2 account for 80−90% of all superlattices that we found in POM/ NC mixtures. Complete STEM and TEM characterization of NaZn13-type POM/NC superlattice is shown in Supporting Information Figure S9. Wide-angle electron diffraction pattern can reveal the internal structure of individual building blocks and can examine the possibility of their preferential orientation within the superlattice.35b Selected area wide-angle diffraction patterns of AlB2- and NaZn13-type superlattices (Supporting Information Figure S8) contain rings corresponding to PbS NCs only, because {Mo132} clusters are internally noncrystalline. Uniform diffraction rings in NaZn13-type lattice indicate random orientation of PbS NCs, independent from the orientation of the superlattice. In contrast, wide-angle diffraction patterns of AlB2-type superlattice contain four arcs of higher intensity for (002) reflections of PbS lattices (d = 2.97 Å), observed in two crystallographic projections ([100] and [111̅ ] of the superlattice. AB5-Type Lattice (Isostructural to CaCu5). At γeff = 0.74, we exclusively find one lattice of CaCu5-type, covering up to 50% of the sample area (Figure 4). Although this structure is so far not predicted to be thermodynamically stable in hard-sphere mixtures, it is one of the most common structures found in NC-NC binary assemblies. In 2002, small regions with AB5 arrangement were found by Shevchenko et al. using mixtures of smaller and larger CoPt3 NCs.41 Redl and co-workers observed AB5 lattice in the mixtures of semiconducting PbSe NCs and magnetic γ-Fe2O3 NCs,1a followed by numerous reports in other NC systems.7,42 In nearly all cases the corresponding size ratios were in the range of 0.65−0.75. CaCu5-type lattice has

Figure 3. (a,b) TEM images at various magnifications of a binary POM/PbS superlattice isostructural with [001]-projected NaZn13 crystal structure, constructed from 6.6 nm PbS NCs and 2.9 nm DDA-encapsulated {Mo132} clusters (γeff = 0.58); (c) image obtained by template analysis of (b); (d) crystallographic model of [100]oriented NaZn13 lattice.

Figure 4. (a,b) TEM images at various magnifications of a binary superlattice isostructural to CaCu5-type lattice oriented along {001} crystal axis, comprising 4.7 nm PbS NCs and 2.9 nm DDAencapsulated {Mo132} clusters (γeff = 0.74); (c) image obtained by template analysis of (b); (d) model of [001]-oriented CaCu5 lattice.

small regions of aperiodic long-range ordered packings with 12fold symmetry, also known as quasicrystals, were observed at γeff = 0.51 (Figure 5). Very similar results were obtained for {Mo132}/CdSe systems (AlB2, NaZn13, and quasicrystalline lattices, Supporting Information Figures S10 and S11) and for assembly of {Mo132} clusters with PbS/CdS NCs (AlB2-type lattice at γeff = 0.46, Supporting Information Figures S12 and S18). Furthermore, {Mo72V30} clusters were cocrystallized with PbS NCs forming AlB2-type superlattice (Supporting Information Figure S13). Notably, the lateral extend of periodic binary superlattices isostructural to AlB2, NaZn13, and CaCu5 can be as large as several micrometers per domain (several million NCs/ domain, Supporting Information Figures S14−18). Furthermore, convenient growth of thin film superlattices at the water−air interface (Supporting Information Figure S18) may be especially suited for device-compatible, large-scale handling. E

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Summary. Our experimental findings show that both POMs and NCs can be combined into long-range ordered periodic and quasicrystalline binary superlattices through the solventevaporation induced crystallization. The integration of POM clusters into NC superstructures may lead to new phenomena arising from the combination of excitonic or plasmonic properties of NCs and redox and catalytic properties of POMs. Our study also suggests that many other cluster species such as fullerenes (C60, C70) and magic-sized metallic and semiconductor clusters may be combined with colloidal inorganic NCs to construct binary superlattices.

also been widely observed in micrometer-sized hard spheres.43 In fact, theoretical calculations suggest that structures that are disfavored solely on space-filling principles, may be stabilized by the extra entropy of mixing.44 Quasicrystals. Samples with γeff = 0.51 in POM/PbS NC system (Figure 5) and with γeff = 0.49 in POM/CdSe system (Supporting Information Figure S11) contained a fraction of aperiodic yet long-range ordered assemblies, known as quasicrystals. This observation is among very few examples of mesoscopic quasicrystals that include all quasicrystalline structures on the length scale larger than atomic lattices. These are NC−NC binary superlattices,5a ABC-type block copolymers,45 dendritic micellar systems,46 and mesoporous silica.47 In all these cases, including POM/NC assemblies reported here, only 12-fold (dodecagonal) symmetries, forbidden in any periodic lattice, were observes, as can be seen from the Fouriertransform patterns (Figure 5c and Supporting Information Figure S11). This is in striking contrast to atomic quasicrystals in which 12-fold (dodecagonal) symmetries are extremely rare48 and mostly metastable. Recently, Lifshitz et al. pointed out that the stability of dodecagonal quasicrystals can be attributed to the existence of two natural length scales in the pairwise interaction potential, combined with effective threebody interactions arising from entropy.49 The maximal lateral extend of POM/NC quansicrystalline assemblies is by far smaller than that of periodic POM/NC lattices: 100−200 nm in quasicrystals versus 5−10 μm in binary POM/NC superlattices. The structure can be visualized by connecting the centers of larger spheres (PbS NCs), leading to a “random” tiling of squares and triangles filling the entire area of the structure (Figure 5b, Supporting Information Figure S11b). So far, a single detailed report on quasicrystals in NC−NC assemblies5a described dodecahedral quasicrystalline ordering at γeff = 0.43 in three systems: 5 nm Au NCs−14 nm Fe3O4, 4.7 nm Au NCs−12.6 nm Fe2O3 NCs, and 3 nm Pd NCs−9 nm PbS NCs. At γeff = 0.43, the quasicrystalline phase and Archimedean tilings were observed at a crossing point of the space-filling curves for the AlB2 and CaB6 phases, at packing density of 0.70. At the crossing point, the translational entropies of the AlB2, CaB6 and dodecagonal phases and Archimedean tilings are very similar.5a Therefore, the quasiperiodicity was suggested to be the result of maximizing the entropy of arrangement of square and triangular “tiles” via multiple degenerate ways of packing. Hence the higher configurational entropy may cause the quasicrystalline state to be more stable than crystalline binary states.5a Talapin et al. also suggested the formation of quasicrystals at γeff = 0.54,5a at which identical packing conditions occur for simple hexagonal and CsCl packings, though less likely than at γeff = 0.43 due to lower packing density of ρ = 0.6. In fact, a later report by Bodnarchuk et al.5b contained examples of dodecagonal quasicrystals comprising 5.2 nm Au NCs and 11.2 nm PbS NCs, which would correspond to γeff ≈ 0.54 assuming ligand shell of ∼1 nm. Our size ratios of 0.51 is intermediate to the ones abovementioned and once again points to complex, presently poorly understood mechanisms underlying the crystal structures in colloidal assemblies. At present stage, the relatively small lateral extend, poor visibility of {Mo132} clusters, and unknown out-ofplane stacking sequence preclude from the accurate assessment of the packing density and stoichiometry of the quasicrystalline packing, and make it difficult to systematically study the effects of kinetic factors and substrate morphology.

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ASSOCIATED CONTENT

S Supporting Information *

Materials, methods, and further details of structural characterization are provided. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: (M.V.K.) [email protected]; (M.I.B.) [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank D. Vanmaekelbergh, C. Murray, R. Nesper, and F. Stellacci for stimulating discussions, M. Wörle for XRD measurements and for help with crystallographic visualization of superlattices, and L. Protesescu for providing highly monodisperse PbS/CdS and CdSe nanocrystals. M.I.B. thanks the Swiss National Science Foundation for the Marie Heim Vögtlin grant. M.V.K. acknowledges partial financial support from ETH Zürich and from the European Union through the FP7 (ERC Starting Grant NANOSOLID, contract number 306733). M.B., F.K., and M.K. acknowledge support of the Electron Microscopy Center of the Swiss Institute of Technology Zürich (EMEZ).

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